1. Nonprofit. A nonprofit company concerned with the school dropout rates in the United States has designed a tutoring program aimed at students between 16 to 18 years old. The National Center for Education Statistics reported that the high school dropout rate in the United States for the year 2000 was 10.9%. One school district, who adopted the use of the nonprofit's tu- toring program and whose dropout rate has always been very close to the national average, reported in 2004 that 175 of their 1782 students dropped out. Is their experi- ence evidence that the tutoring program has been effec- tive? Explain.
2. Real estate. A national real estate magazine adver- tised that 15% of first-time home buyers had a family income below $40,000. A national real estate firm believes this percentage is too low and samples 100 of its records. The firm finds that 25 of its first-time home buyers did have a family income below $40,000. Does the sample suggest that the proportion of first-time home buyers with an income less than $40,000 is more than 15%? Comment and write up your own conclusions based on an appropriate confidence interval as well as a hypothesis test. Include any assumptions you made about the data.